Problem

3. $M = \begin{pmatrix} k & k \\ 3 & 5 \end{pmatrix}$ where $k$ is a non-zero constant

(a) Determine $M^{-1}$, giving your answer in simplest form in terms of $k$.

Hence, given that $N^{-1} = \begin{pmatrix} k & k \\ 4 & -1 \end{pmatrix}$

(b) determine $(MN)^{-1}$, giving your answer in simplest form in terms of $k$.